Secondary Sample Tasks
The secondary sample tasks, with development led by the Dana Center, are a rich set of sample instructional tasks that exemplify expectations leading to Achieve's college- and career-ready standards. These tasks cover a range of student expectations, include a variety of solution strategies, and correlate to other documents being created for this work (for example, the model courses and the Algebra II end-of-course exam).
- Archeological Similarity. This task allows students to use their knowledge of similar triangles, the Pythagorean theorem, and the converse of the Pythagorean theorem to solve a historically and culturally interesting problem while at the same time developing their understanding of mathematical proofs.
- Autobahn. Students use calculations with rational numbers to compute average speeds.
- Bighorn Sheep. Students model a situation with exponential functions in order to make predictions
and solve problems.
- Chinese Restaurant. This task allows students to see how geometric constructions can be used to inform decisions about where to locate a business. It provides opportunities to use pencil-and-paper construction or geometric software (or both) to solve the problem and software to explore or verify conjectures.
- Click It. This task goes beyond analyzing data by connecting the various discrete steps involved in designing and conducting a study.
- Common Differences. This task illustrates mathematical reasoning using a general conjecture that students can prove by building from specific examples to a general case.
- Cones Launch. This task allows students to connect algebra and geometry by using geometric formulas and spatial skills to solve a problem in a real-world context. It allows for varying levels of difficulty and can be accessible to a wide range of students.
- Congruence Challenge. This task challenges students to apply what they know about parallel and intersecting lines, parallelograms, and the angles and segments related to these figures to solve a geometric problem in a purely mathematical context.
- Counting Cubes. This task asks students to create a pattern using multiple representations (pictures, tables, graphs, and algebraic rules). Students engaged in the task will generate various ways to describe the pattern depending on how they visualize the situation, which will lead to equivalent, but different, expressions.
- Cycling Situations. This task, accessible to beginning algebra students, builds an understanding of what it means to solve systems of linear equations by using diagrams, tables, and graphs.
- Equal Salaries for Equal Work?. This task asks students to compare additive and multiplicative growth (represented by linear and exponential models) to make predictions and solve problems
- Function Transformations. Students use multiple representations to discover the transformational patterns
of a piecewise function.
- Gamers. This task provides a context for using a two-way frequency table and a Venn diagram to explore the relationships among probabilities.
- How Odd . . . Students (and adults) often confuse probability and odds, and misuses of these terms are common in the media. This task allows a discussion of the difference between and the relationship between these two concepts using interesting contexts found in the media.
- Is Your Score Normal? This task provides students with a relevant context (PSAT scores) as they examine a normal distribution and use it to determine the probability of individual results.
- King's Deli. Students see how calculations with rational numbers can help deal with practical problems from real-world situations,
- Leo's Painting. Students integrate algebra and geometry as they generate a quadratic
inequality from a proportional relationship.
- Match That Function. This task requires students to analyze a situation, describe the appropriate function for the situation using multiple representations, and make connections among the representations. The task provides an opportunity to compare various types of functions.
- Neighborhood Park. Students investigate the effects of a scale factor, r, on length, area and volume in a problem-solving context.
- Out of the Swimming Pool. This task illustrates that different but equivalent expressions can be used in a function rule to provide valuable information about the context of the problem.
- Regional Triangles. This task may be used with students who have various levels of geometric understanding to emphasize geometric vocabulary, apply basic theorems involving circles, make conjectures, and justify or prove conjectures.
- Rock, Paper, Scissors. Students use tree diagrams to determine the probabilities used to decide if two versions of Rock, Paper, Scissors are fair.
- Rolling for the Big One. This task helps students understand the different types of probabilities related to more than one event.
- A Safe Load. This task allows students to investigate the importance of using a reasonable degree of precision in a real life situation by allowing them to see how the degree of precision can dramatically affect the results.
- Satellite. This task allows students to use trigonometry and properties of circles and triangles to find distances.
- Season Pass. This task asks students to analyze and fit a mathematical model to data in order to answer questions about maximizing revenue.
- Summer Business! This task allows the student to see how linear programming can be used to maximize earnings in real world small business applications.
- Talk Is Cheap. This task can be used to introduce students to functions in a realistic setting—choosing a cell phone plan given certain conditions. Students gain experience working with decimals and translating among different representations of linear functions.
- Television and Test Grades. This task allows students to analyze data sets that they might typically collect to set up scatter plots. Students then determine linear trends and lines of good fit when they exist.
- You're Toast, Dude! Students extend their understanding of functions to rational functions by exploring average cost. They gain experience in moving between a problem context and its mathematical model in order to solve problems and make decisions.